Asphere and a cylinder have the same radius and height. the volume of the cylinder is 50ft cubed. what is the volume of the sphere?

Start with the formulas for the volumes of the sphere and cyl. respectively:

Vs = (4/3)*pi*r^3                        Vc = pi*r^2*h

Here, sphere and cyl. have the same radius and height.  Thus, the diam. of the sphere, d = 2r, has the same value as does h.

Thus, Vs = (4/3)*pi*r^3    and     Vc = pi*r^2*(2r) = 50.  Thus, pi*r^3 = 50, or
                                                                                                     r^3 = 50/pi

Then Vs = (4/3)(pi)*(50/pi) = 200/3 ft^3

Unfortunately, this doesn't agree with any of the answer choices, 'though it's close to given choice 100/3 ft^3, off by a factor of 2.

The trick here is to eliminate variables (especially the cyl. ht., h) and to make appropriate substitutions.